Add web “continue session” flow with part-aware terminal startup

[Codex]

Browser users lacked a way to resume a paused session as a new terminal part; the API also needed guards and parts_count updates.

• API: POST /api/session/{name}/continue now creates the next part, writes signed session_meta with parts_count, guards active terminals with 409, and launches a PTY-backed shell (bash/sh fallback if zsh missing) returning {session, part, status, pid}.
• Terminal UI: Session page gains a Continue button, part badge, and part-aware terminal start/stop/write/WebSocket calls so the live terminal attaches to the newest part.
• Core/session: Shared helpers to compute next part, patch parts_count, and include parts_count in part metas.
• Docs/Changelog: Updated README and changelog to describe the continue behavior and response shape.

// Session page JS
async function gsContinueSession() {
  const resp = await fetch(`/api/session/${gsSessionPath}/continue`, { method: "POST" });
  const payload = await resp.json();
  gsSetTerminalPart(Number(payload.part));
}

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